Recently, power electronics equipments for flexible AC power transmission systems (FACTS) have been investigated and applied to practical systems. A transformerless reactive series compensator is one of these equipments and is effective to perform a power flow control as was explained above. Since the transformerless reactive series compensator does not comprise a transformer its size is small and it can be advantageously used.
FIGS. 1a and 1b respectively show a typical configuration of a power transmission system comprising two AC power systems 1a, 1b coupled to each other through power transmission lines 2a, 2b having a respective inductance L.sub.AC and resistance R.sub.AC. As indicated in FIG. 1a and FIG. 1b, the power transmission system may be a single phase system or a three-phase system. Whilst in the single phase system only one series compensator 3 need to be provided, in the three-phase system a plurality of series compensators 3 are respectively serially inserted as shown in FIG. 1b. Reference numerals 3a, 3b respectively show the terminals at which the respective series compensator (or compensators) are serially inserted.
As shown in FIG. 2, a typical series compensator 3 comprises a starting switch 4, a filter 12, an inverter 7, a DC capacitor C.sub.DC, a control means C, a saw-tooth generator 10 and a modulation signal generation means 11. The inverter 7 comprises four thyristors 5a, 5b, 5c, 5d respectively controlled by a PWM control signal SW.sub.5a, SW.sub.5b, SW.sub.5c, SW.sub.5d output by the control means C.
Whilst the expression "thyristor" is usually a device whose turn-off is not controllable, in FIG. 2, since PWM is used for the inverter, a gate turn-off type thyristor is employed. Since a GTO (gate turn-off thyristor), a GCT (gate commutated thyristor) and an IGBT (insulated gate bipolar transistor) are also generally possible for operating as the kind of switching power device in FIG. 2, hereinafter it is assumed that the expression "thyristor" comprises all such switching power devices.
Each thyristor has connected anti-parallely thereto a diode 6a, 6b, 6c, 6d. The filter 12 comprises two reactors 9b, 9a and a capacitor 8 for filtering higher order harmonics which are generated by the PWM control of the inverter 7. The filter terminals are connected to the respective interconnections of the thyristors 5a, 5b and of the diodes 6a, 6b and the thyristors 5c, 5d and the diodes 6c, 6d. The DC capacitor C.sub.DC is connected at the other terminals of the thyristors and the diodes.
The circuit configuration of the series compensator 3 is conventional and is for example described in the European patent applications EP 98 116 096.3 and EP 98 106 780.4 by the same applicant. These two patent applications in particular describe the start and stop control of the series compensator 3.
A PWM control of the inverter 7 is carried out as principally shown in the diagram of FIG. 3. A modulation signal generation means 11 in FIG. 2 generates a sinusoidal modulation signal m and the saw-tooth generator 10 outputs two saw-tooth carrier signals cs1, cs2. A PWM control signal SW.sub.5a, SW.sub.5d is generated by comparing the modulation signal m with the respective carrier signal cs1, cs2. That is, when the modulation signal amplitude is larger than the carrier signal cs1 amplitude, then the PWM switching signal SW.sub.5a is on and it is off if the modulation signal amplitude is smaller. Similarly, if the amplitude of the modulation signal is larger than the inverted carrier signal cs2, then the other PWM switching signal SW.sub.5d is switched from ON to OFF. The PWM signals SW.sub.5a, SW.sub.5d are used to trigger the thyristors 5a, 5d. It should be noted that a similar control applies to the thyristors 5b, 5c which is, however, not described here for simplicity.
Assuming that the DC capacitor C.sub.DC was charged to u.sub.DC the output voltage u.sub.c at the connection terminals 3a, 3d will have a waveform as shown in FIG. 3 in the bottom graph. It will be appreciated that by changing the respective amplitudes of the modulation signal and/or the carrier signal and/or by changing the phase of the modulation signal and/or the carrier signal, different waveforms of the output voltage u.sub.c (hereinafter also called the inverter terminal voltage or compensator output voltage) can be achieved. Comparing FIG. 3 with FIG. 2 it can be seen that essentially the output voltage u.sub.c is the voltage applied to the terminal 3a, 3b.
Whilst from FIG. 3 it only appears as if the terminal voltage u.sub.c changes due to the PWM control of the inverter 7, of course the line current i would also change since current and voltage are linked through the coupling effects due to the line impedance L.sub.AC. The simultaneous effects of the PWM control on the line voltage and the line current will be explained now.
FIG. 4a shows a summary diagram of the essential parts of FIG. 2 necessary for explaining the current and voltage control. FIG. 4b shows the principle phasor diagram for FIG. 4a. As was the case in FIG. 1a, also in FIG. 4a the compensator 3 is serially connected between the power transmission lines 2a, 2b which are connected to the AC power systems 1a, 1b. For the purpose of explaining the current and the voltage control with respect to their phase relationships it is not necessary to consider explicitly the line impedance R.sub.AC, although it should be understood that of course the line impedance R.sub.AC is also present in FIG. 4a. The inverter control is schematically illustrated with the block to which the reference numeral 7 has been attached. A modulation signal m is applied in order to perform the PWM control. u.sub.L is the voltage occurring as a result of the line impedance L.sub.AC, i is the line current, i.sub.DC is the current flowing through the DC capacitor C.sub.DC, u.sub.DC is the voltage over the DC capacitor C.sub.DC and u.sub.c is the output voltage of the series compensator 3. Furthermore, u.sub.x is the overhead voltage which is a difference voltage between the AC sources. For simplicity reasons the leakage conductance in the DC side which could include the switching losses, leakage losses of capacitors and/or losses of DC filters (essentially a parallel resistance to the DC capacitor C.sub.DC is not necessary to be considered for the phase relationships.
FIG. 4b shows a principle phasor diagram and the voltages explained with reference to FIG. 4a are shown therein. The compensator 3 can output an output voltage u.sub.c of arbitrary phase with limited amplitude using the DC capacitor voltage u.sub.DC. FIGS. 5(a), 5(b) and FIG. 5(c) respectively show the cases for no compensation, capacitive operation and inductive operation when controlling the line current i. That is, when the compensator 3 injects a zero voltage u.sub.c into the line, then the inductance voltage u.sub.L is the same as the overhead voltage u.sub.x (FIG. 5(a)). In this case, the line current i flows through the transmission line with a 90.degree. phase lag with respect the inductance voltage u.sub.L.
When the compensator 3 injects a capacitive voltage u.sub.c which leads 90.degree. to the line current i, then the inductance voltage u.sub.L increases and therefore also the line current i is increased (FIG. 5(b)).
On the other hand, when the compensator 3 injects an inductive voltage to the line (u.sub.c is in-phase with the inductance voltage u.sub.L), the inductance voltage u.sub.L is decreased and therefore also the line current i is decreased (FIG. 5(c)). Thus, the first purpose of the compensator 3 is that the line current i can be controlled (increased/decreased) by the voltage (by the amplitude and the phase of the compensator output voltage u.sub.c) output by the compensator 3. Furthermore, of course a skilled person realizes what has been described above for a single phase can be performed in the same manner for a three-phase system.
Of course, the control in FIG. 5 can only be carried out if the DC capacitor C.sub.DC has been charged to the predetermined voltage u.sub.DC since otherwise no injection of voltage would be possible into the line. Instead of using a battery or another power source, it is advantageous to also control the compensator 3 such that a power flow from the line to the DC capacitor C.sub.DC is effected. Such a charging or active power flow from the line to the capacitor is explained with reference to FIG. 6 and FIG. 7.
As mentioned before, a charging of the DC capacitor C.sub.DC requires an active power flow from the transmission lines 2a, 2b to the DC capacitor C.sub.DC through the inverter 7. In order to take the active power from the power system 1a, 1b, the compensator 3 has to feed the active component of the applied AC voltage u.sub.c to the DC capacitor C.sub.DC.
In steady state conditions, as already explained with reference to FIG. 5(c) and as shown also in FIG. 6(a), the compensator 3 outputs a reactive voltage u.sub.c which has a 90.degree. difference phase to the line current i. This situation is present in the initial state and the final state of charge control as shown with FIGS. 6(a) and 6(c).
When the compensator 3 outputs the active component in a short duration for taking in active power, the inductance voltage is also changed transiently as shown in FIG. 6(b). The transient inductance voltage includes a di/dt component and a .omega.Li component. When the di/dt component is generated, the .omega.Li component is influenced. Then, the variation of the .omega.Li component influences the di/dt component and the line current fluctuates in an oscillation manner as shown in FIG. 6(b). Consequently, the charging process does not only influence the capacitor voltage but also the line current. The reason is the coupling effect through the line inductance L.sub.AC as can be understood from considering the dynamic behavior of the currents and voltages.
Namely, a voltage equation of the inductance L.sub.AC can be written as follows. EQU L.sub.AC (di/dt)=u.sub.AC (1.1)
where L.sub.AC, i and u.sub.AC are the line inductance, a line current and the inductance voltage. If a rotational reference frame is introduced whose frequency is .omega. in a steady-state condition as EQU i=I.sub.d cos (.omega.t)-I.sub.q sin (.omega.t) (1.2) EQU u.sub.AC =U.sub.d cos (.omega.t)-U.sub.q sin (.omega.t) (1.3)
the voltage equation (1.1) can be decomposed in component equations as follows: EQU L(dI.sub.d /dt)=.omega.LI.sub.q +U.sub.d (1.4) EQU L(dI.sub.q /dt)=-.omega.LI.sub.d +U.sub.q (1.5)
It can now be understood, as shown in FIG. 6(b) that if U.sub.d (the active part of the applied voltage) is changed, then also I.sub.d (the active part of the current) varies and I.sub.q (the reactive part of the current) is also influenced.
The coupling of a line current control to a DC voltage is illustrated in FIG. 7. A rapid change of the reactive component of the compensator voltage by the line current controls generates a di/dt component of an inductor voltage. Therefore, the line current phasor i moves towards the direction of the change first. Then, the .omega.Li component and di/dt component influence each other with the same mechanism but opposite coupling. As a result, the line current has a fluctuation and an active component which is a in-phase component to the compensator voltage. This active component now causes an active power flow from the power transmission line to the DC capacitor C.sub.DC in the transient state as shown in FIG. 7(b). However, if the line current is controlled, obviously also the DC voltage is influenced by the line current control.
As can be understood from the above description of FIGS. 4, 5, 6, 7, the main purpose of a controller for the series compensator is to perform a control to increase/decrease the line current as shown in FIG. 5 and to charge the DC capacitor C.sub.DC by allowing an active power flow to the DC capacitor C.sub.DC as in FIGS. 6, 7. Such controllers will be explained hereinafter.